Ar N2 System Research Articles

Rotational excitation of diatomic molecules in collisions with atoms

The rate constants for rotational excitation, the coefficient of RT diffusion for the Ar-N2 system, and the rotational relaxation time in N2 are calculated using the quasiclassical approximation.

Angular and rotational energy moments of cross sections in atom–diatom scattering

The evaluation of the various averages of the rotationally inelastic cross sections which appear in the kinetic theory developments of Wang Chang, Uhlenbeck, and deBoer is discussed and carried out numerically. The generalized phase shift (GPS) approach is used to obtain the rotational energy moments of the degeneracy averaged cross sections. These quantities are developed as power series in the ’’strength’’ of the anisotropic portion of the interaction potential, and the first few terms are evaluated in the classical limit. A nonspherical model potential for the interaction of an atom and a homonuclear diatomic molecule is introduced, and the ’’cross sections’’ are numerically evaluated for five sets of model parameters. One choice of the parameters represents the Ar–N2 system, and the other choices are used to examine the effects on the scattering results of varying specific molecular quantities.

Quenching of the diffraction oscillations in the Ar–N2 total differential cross section

The quenching of diffraction oscillations in the Ar-N2 system is investigated computationally. (AIP).

Surprisal analysis of classical trajectory calculations of rotationally inelastic cross sections for the Ar–N2 system; influence of the potential energy surface

Rotationally inelastic Ar–N2 scattering on two different empirical potential energy surfaces has been investigated by the classical trajectory method. For each potential surface, state-to-state rotational transition cross sections σj′j (E) have been calculated at five total energies E and several initial rotational quantum states j of the N2. Results obtained from the two potentials differ significantly with respect to final rotational state distributions, but the total inelastic cross sections are very similar. Consideration of the moments of the rotational energy transfer leads to the conclusion that the potential surface of Kistemaker and de Vries is the preferred one to represent the Ar–N2 interaction. A surprisal analysis of the computed cross sections has been carried out. At energies below ?3000 K, near-linear surprisal plots are obtained, as found earlier by Levine, Bernstein, Procaccia et al., thus confirming the exponential gap law of Polanyi, Ding, and Woodall for rotational relaxation. Complete cross section matrices (at a given E) can thereby be generated from a two-parameter surprisal fit of a single column of a σj′j matrix (or even from a classically derived first moment from the state j=0). As expected, the rotational surprisal parameter ϑR is essentially independent of j, but it shows a significant, positive E dependence and differs in magnitude for the two potentials.

Transport Properties of a Gas of Diatomic Molecules. V. GPS Calculation of the Rotational Relaxation Time of the Ar–N2 System

The moments of the probability density function for rotationally inelastic scattering of the Ar–N2 system were computed, in Paper XVI of a series on molecular collisions, by both generalized phase shift (GPS) and classical trajectory (CT) methods. In the present paper, it is shown that inclusion of the term of zero order in h/ in a semiclassical expansion of the generalized phase shift modifies the classical limit expressions for the moments. The Ar–N2 system is reconsidered and the first and second moments calculated to the lowest nonzero order in the anisotropy of the interaction potential. The results of this calculation indicate a marked improvement of the first moment over the previous GPS results as compared with the CT results. The development is extended by integrating the moments over the impact parameter and the translational and rotational energies to obtain rotational collision numbers for the Ar–N2 system. These collision numbers are compared with those obtained by classical trajectory methods.

Transport Properties of a Gas of Diatomic Molecules. VI. Classical Trajectory Calculations of the Rotational Relaxation Time of the Ar–N2 System

The rotational relaxation time of nitrogen in an excess of argon was computed by a fully classical, numerically exact procedure, starting from an estimated anisotropic potential for the Ar–N2 system. The method involves integration of the second moment of the rotational inelasticity probability density function P(Δ Erot) over the impact parameter of the collision and a Boltzmann distribution of translational and rotational energies. Confirmatory results were obtained from an integration of the first moment. Both moments of P(Δ Erot) were evaluated by the classical trajectory CT) method of a previous paper by Pattengill et al. The CT results, extrapolated to the limit of weak anisotropy, agree well with those of the classical generalized phase shift approximation discussed in the preceding paper (V). The present results for the relaxation time Pτ vary, over the temperature range 200–400°K, from 8 to 20× 10−10 atm· sec, corresponding to rotational relaxation Z numbers from 6 to 10.

Rotational Excitation of a Rigid Rotor: Comparison of Two Approximate Classical Models with Exact Classical Results

A rigid body model and a perturbation technique are used to measure the rotational excitation of a rigid rotor in the determination of the moments of fractional rotational energy transfer in the Ar-N2 system. A table of data is included to compare the obtained results with exact results, showing the failure of the perturbation model to yield correct results.

Molecular Collisions. XVI. Comparison of GPS with Classical Trajectory Calculations of Rotational Inelasticity for the Ar–N2 System

The classical limit of the ``infinite order'' generalized phase shift (GPS) treatment of rotationally inelastic atom-molecule collisions was put into computationally feasible form in Paper XV of this series. It is now applied to a model problem intended to approximate thermal scattering of the Ar–N2 system (collisional energy of 32kT at 300°K), at the same time comparing its predictions with exact classical trajectory (CT) results. This comparison indicates that the present version of the GPS method over-estimates the rotational excitation and underestimates the de-excitation, while maintaining the total inelasticity at approximately the correct (CT) value. An approximate ``quantization'' of the classical results leads to an estimate of the quantal cross sections corresponding to changes by ±2, ±4, and ±6 from an initial rotor quantum state l¯=10. It is found that most of the total inelastic crosssection (of some 32 Å2) arises from the first-order-allowed transitions (Δ l=± 2).

Phase Diagram of Argon—Carbon Monoxide

The phase diagram Ar–CO has been determined by cooling curves and x-ray diffraction. Like the Ar–N2 system, a solid solution of hcp structure extends over essentially the entire range of concentration at temperatures just under the solidus, but unlike the Ar–N2 system, the hcp phase decomposes (eutectoidally) into a fcc Ar-rich phase and a primitive cubic CO-rich phase at 53°K; the eutectoid point is at 66% CO. The miscibility gap at 53°K extends from 5% to 85% CO and is probably complete at 0°K. There are quite extensive two-phase regions between the phases in the solid state, which were not found in the Ar–N2 system. There is again an indication that Ar would have the hcp structure just a few degrees above the melting point if melting did not intervene. Liquidus and solidus temperatures for Ar–CO reach a minimum (65°K) near 60%—70% CO. Lattice constants for the different phases are presented.